Problem: Solve for $x$ and $y$ using substitution. ${6x+6y = 0}$ ${y = -3x+2}$
Answer: Since $y$ has already been solved for, substitute $-3x+2$ for $y$ in the first equation. ${6x + 6}{(-3x+2)}{= 0}$ Simplify and solve for $x$ $6x-18x + 12 = 0$ $-12x+12 = 0$ $-12x+12{-12} = 0{-12}$ $-12x = -12$ $\dfrac{-12x}{{-12}} = \dfrac{-12}{{-12}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {y = -3x+2}\thinspace$ to find $y$ ${y = -3}{(1)}{ + 2}$ $y = -3 + 2$ $y = -1$ You can also plug ${x = 1}$ into $\thinspace {6x+6y = 0}\thinspace$ and get the same answer for $y$ : ${6}{(1)}{ + 6y = 0}$ ${y = -1}$